I have two polynomials: $\;A(x) = \sum a_i\;x^i$, $\quad B(x) = \sum b_i\;x^i$.
Given $A(x)$, $B(x)$, I want to compute $\;C(x) = $MIN$(A(x), B(x)) = c_i\;x^i$ where $c_i = $MIN$(a_i, b_i)$.
How can I do it automatically in Mathematica?
Another one, possibly shorter, which works with any number of unequal degree polys:
Works for any number of polys:
With exact coefficient lists you can do the following:
Update: generalization to any number of nonaligned polynomials (inspired by ubpdqn)
Here is the way to work with any number of polynomials of different orders:
Let's choose a list of polynomials, e.g.
then we have
If we know that orders of the polynomials are equal, for example:
this is another approach:
On the off chance that the polynomials have unequal highest degree (hence unequal coefficient list lengths):